Geomagnetic sensor calibration apparatus and method thereof

ABSTRACT

A geomagnetic sensor calibration apparatus includes a geomagnetic sensor which measures at least one value of Earth&#39;s magnetic field, an initial point estimator which estimates first central points regarding the at least one value of the Earth&#39;s magnetic field by using a first linear function, a central point estimator which estimates second central points by using a second linear function and the estimated first central points, and a controller which determines whether calibrating of the geomagnetic sensor is necessary based on the estimated first central points and controls the central point estimator to estimate second central points based on whether calibration is determined to be necessary.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority from Korean Patent Application No.10-2013-0005503, filed on Jan. 17, 2013 in the Korean IntellectualProperty Office, the disclosure of which is incorporated herein byreference in its entirety.

BACKGROUND

1. Field of the Invention

Apparatuses and methods consistent with exemplary embodiments relate toa geomagnetic sensor which measures the magnitude and direction of theEarth's magnetic field, and more specifically, to a geomagnetic sensorcalibration apparatus and method which correct errors of geomagneticsensors.

2. Description of the Related Art

Various types of electronic devices including devices having globalpositioning system (GPS) functions and compass functions have beendeveloped and supplied with the development of electronic technologies.In order to perform these functions, a process of calculating azimuth isrequired. Gyro sensors or geomagnetic sensors are widely used tocalculate azimuth. For example, gyroscopes and geomagnetic sensors aremounted on electronic devices, such as smart phones or tablet personalcomputers (PCs) and perform various services or functions includingsensing user movements and estimating direction of devices.

A gyroscope sensor calculates rotating angular velocity by calculatingCoriolis force. When a gyroscope is used, velocity is calculated bymeasuring and integrating accelerations, and displacement information isobtained by double integrating the calculated velocity.

A geomagnetic sensor measures the geomagnetic field with a method ofmeasuring voltage values induced by the geomagnetic field by using afluxgate of other device. The geomagnetic sensor may be implemented withtwo axes or three axes. Because output values calculated from each axisof the geomagnetic sensor vary according to the magnitude of surroundinggeomagnetic fields, normalization, in which output values of thegeomagnetic sensor are mapped within a preset range, for example, from−1 to 1, may be performed. Normalization is performed by usingnormalizing factors, such as scale values or offset values. To calculatenormalizing factors, output values are calculated while rotating thegeomagnetic sensor several times, and maximum and minimum values aredetected among the output values. Values normalized by using normalizingfactors are utilized in calibrating azimuth.

However, offset values among normalizing factors are often distorted dueto influences of surrounding environment factors which affect magnetism.FIG. 1 is an illustration which simplifies and expresses magneticdistortion on dimensional coordinates.

There are soft iron effects and hard iron effects for magneticdistortion which influence the geomagnetic sensor. Effects by soft ironchange the scale of sensor values and effects by hard iron influence theoffset of sensor values. Because effects by soft iron are usuallyminimal, to calibrate errors of the geomagnetic sensor effects by hardiron are discussed.

For example, when the geomagnetic sensor is mounted within mobileelectronic devices, such as cellular phones, offset values may bechanged when substituting a battery or closing and opening LCD folder.Offset values may also be changed when turbulent material, such asobjects with strong magnetic properties or steel structures are placednear the geomagnetic sensor. When normalization is performed by usingdistorted offset values, normalized values are distorted. Therefore,finally calculated azimuth includes errors.

FIG. 2 is a diagram which illustrates effects by hard iron onthree-dimensional coordinates of X, Y, and Z.

Korean Patent No. 10-0831373 discloses that a geomagnetic sensor iscalibrated by using offset values, average values, and standarddeviation values so as to account for errors caused by effects of hardiron in sensed values of the geomagnetic sensor.

According to KR 10-0831373, a three-axis geomagnetic sensor calculatesoutput values corresponding to surrounding magnetics by using a fluxgateof X, Y, and Z axes that are orthogonally crossed. The output valuesfrom the three-axis geomagnetic sensor are normalized by mapping each ofoutput values in the fluxgate of X, Y, and Z axes within a preset range,for example, from −1 to 1. Offset values and scale values used innormalization are previously established and stored in an internalmemory.

Distance (r_(e)) between output values (X, Y, Z) of the three-axisgeomagnetic sensor and preset offset values (X_(0P), Y_(0P), Z_(0P)) canbe expressed with the following mathematical formula:

r _(p)=√{square root over ((X−X _(0p))²+(Y−Y _(0p))²+(Z−Z_(0p))²)}{square root over ((X−X _(0p))²+(Y−Y _(0p))²+(Z−Z_(0p))²)}{square root over ((X−X _(0p))²+(Y−Y _(0p))²+(Z−Z_(0p))²)}  [Formula 1]

According to Formula 1, when distance (r_(p)) is greater than allowablerange (α), it is determined that the geomagnetic values are distortedand calibration is performed. The above offset values are central pointsof a sphere which indicate critical error values calculatedstatistically. The allowable range can be established with variousvalues, such as 1 or 1±0.1 according to the area in which the electronicdevice having the three-axis geomagnetic sensor is used or according tothe use objectives of electronic devices.

When distortion is determined to occur, sampling sensed geomagneticvalues is performed to calibrate errors. Sampling is randomly performedwhenever the geomagnetic sensor device moves within preset time. KR10-0831373 suggests a method of keeping a distance between respectivesampled values to be more than a preset distance. In other words,KR10-0831373 selects sampled values only out of critical distance.

After sampling, the mean (mean(r_(p))) and standard deviation(std(r_(p))) of distances (r_(p)) between output values (X, Y, Z) to besampled in the geomagnetic sensor and the above offset values arecalculated. If any one of the mean (mean(r_(p))) and the standarddeviation (std(r_(p))) is greater than a preset value, it is determinedthat distortion has occurred.

In order to calibrate the three-axis geomagnetic sensor, athree-dimensional sphere which has central points (X₀, Y₀, Z₀) andradius (r) can be modeled according to the following mathematicalformula:

(X−X ₀)²+(Y−Y ₀)²+(Z−Z ₀)² r ²  [Formula 2]

The least square method is used to calculate central points (X₀, Y₀, Z₀)from values of the three-axis geomagnetic sensor. Preset offset values(X_(0P), Y_(0P), Z_(0P)) are established as initial values of centralpoints (X₀, Y₀, Z₀), and radius (r) is a constant value established asthe radius of a magnetic sphere based on preset offset values (X₀, Y₀,Z₀). The central points are estimated with a Gauss-Newton algorithm.

However, the method of calibrating a geomagnetic sensor proposed by KR10-0831373 lacks preciseness in estimating central points because theinitial values established based on specific conditions, and used in thecalibration calculations, are fixed. Therefore, a method of calibratinga geomagnetic sensor more precisely is necessary.

SUMMARY

Exemplary embodiments address the above disadvantages and otherdisadvantages not described above. Also, the exemplary embodiments arenot required to overcome the disadvantages described above, and anexemplary embodiment may not overcome any of the problems describedabove.

One or more exemplary embodiments provide a geomagnetic sensorcalibration apparatus and method which can perform precise errorcalibration by estimating initial central points of a sphere whichmodels sensed geomagnetic values by using linear functions andestimating final central points by using the estimated initial centralpoints.

According to an aspect of an exemplary embodiment, there is provided ageomagnetic sensor calibration apparatus including a geomagnetic sensorconfigured to measure at least one value of Earth's magnetic field, aninitial value estimator configured to estimate first central points fromthe at least one measured value of the Earth's magnetic field by using afirst linear function, a central point estimator configured to estimatesecond central points by using a second linear function and theestimated first central points, and a controller configured to determinewhether calibration of the geomagnetic sensor is necessary based on theestimated first central points, and control the central point estimatorto estimate second central points based on a result of thedetermination.

The at least one value of the Earth's magnetic field may be expressedwith coordinates in an X, Y, and Z axes of dimensional coordinates.

The first linear function may linearize a function:

f=r _(i) ² −r ²,

wherein

r _(i)=√{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)²)},

(X−X ₀)²+(Y−Y ₀)²+(Z−Z ₀)² =r ²,

(X_(i), Y_(i), Z_(i)) are coordinate values which are sampled at an i-thnumber of the geomagnetic sensor,

(X₀, Y₀, Z₀) are the estimated first central points,

n is a predetermined integer, and

1≦i≦n.

Further, the second linear function may linearize a minimized function:

d _(i) =r _(i) −r ₀,

wherein

r _(i)=√{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)²)},

(X_(i), Y_(i), Z_(i)) are coordinate values which are sampled at an i-thnumber of the geomagnetic sensor,

(X₀, Y₀, Z₀) are the estimated first central points,

r₀ is a radius of a sphere having the estimated first central points,

n is a predetermined integer, and

1≦i≦n.

Further, the first linear function may linearize a minimized function:

d _(i) =r _(i) − r ,

wherein

r _(i)=√{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)²)},

(X_(i), Y_(i), Z_(i)) are coordinate values which are sampled at an i-thnumber of the geomagnetic sensor,

(X₀, Y₀, Z₀) are the estimated first central points,

r is a constant value indicating a radius of a sphere having theestimated first central points,

n is a predetermined integer, and

1≦i≦n.

The controller may be further configured to calibrate central points byusing a following formula:

${{\hat{M}}_{b} = {{M_{b} - M_{0}} = \begin{bmatrix}{X - X_{0}} \\{Y - Y_{0}} \\{Z - Z_{0}}\end{bmatrix}}},$

wherein M₀=[X₀, Y₀, Z₀]^(T) are coordinate values indicating centralpoints estimated by the central point estimator, and

M_(b)=[X, Y, Z]^(T) are output values of the geomagnetic sensor.

The controller may be further configured to calculate a mean value and astandard deviation value of distances between a plurality of samplingcoordinates output from the geomagnetic sensor and the estimated firstcentral points, and determine that calibrating is necessary based onwhether at least one of the calculated average value and standarddeviation value exceeds a preset value.

The geomagnetic sensor may include a fluxgate of X, Y, and Z axes whichare arranged orthogonally to each other, a driving signal generatorconfigured to provide driving signals to the fluxgate of X, Y, and Zaxes, a signal processor configured to, when the fluxgate of X, Y, and Zaxes is driven by the driving signals and outputs electrical signalscorresponding to a surrounding magnetic field, convert the electricalsignals to digital signals and output the digital signals, and ageomagnetic sensor controller configured to perform normalization to mapoutput values of the signal processor within a certain range by usingoffset values and preset scale values, and output normalized three-axisoutput values.

The controller may be further configured to calculate a pitch angle anda roll angle of the geomagnetic sensor calibration apparatus, andcalculate azimuth by using the at least one measured value of theEarth's magnetic field, the pitch angle, and the roll angle.

According to an aspect of another exemplary embodiment, there isprovided a geomagnetic sensor calibration method including measuring atleast one value of Earth's magnetic field, estimating first centralpoints from the at least one measured value of the Earth's magneticfield by using a first linear function, and estimating second centralpoints by using a second linear function and the estimated first centralpoints.

The values of the at least one measure value of the Earth's magneticfield may be expressed with coordinates in a X, Y, and Z coordinatespace.

Further, the first linear function may linearize a function:

f=r _(i) ² −r ².

wherein

r _(i)=√{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)²)},

(X−X ₀)²+(Y−Y ₀)²+(Z−Z ₀)² =r ²,

(X_(i), Y_(i), Z_(i)) are coordinate values which are sampled at an i-thnumber of the geomagnetic sensor,

(X₀, Y₀, Z₀) are the first estimated central points,

n is a predetermined integer, and

1≦i≦n.

Further, the second linear function may linearize a minimized function:

d _(i) =r _(i) −r ₀,

wherein

r _(i)√{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)²)},

(X_(i), Y_(i), Z_(i)) are coordinate values which are sampled at an i-thnumber of the geomagnetic sensor,

(X₀, Y₀, Z₀) are the first estimated central points,

r₀ is a radius of a sphere having the estimated first central points,

n is a predetermined integer, and

1≦i≦n.

Further, the first linear function may linearize the minimized function:

d _(i) =r _(i) − r ,

wherein

r _(i)=√{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)²)},

(X_(i), Y_(i), Z_(i)) are coordinate values which are sampled at an i-thnumber of the geomagnetic sensor,

(X₀, Y₀, Z₀) are the first estimated central points,

r is a constant value indicating a radius of a sphere having theestimated first central points,

n is a predetermined integer, and

1≦i≦n.

The geomagnetic sensor calibration method may further includecalibrating central points by using a formula:

${{\hat{M}}_{b} = {{M_{b} - M_{0}} = \begin{bmatrix}{X - X_{0}} \\{Y - Y_{0}} \\{Z - Z_{0}}\end{bmatrix}}},$

wherein M₀=[X₀, Y₀, Z₀]^(T) are coordinate values of the second centralpoints estimated by the central point estimator, and

M_(b)=[X, Y, Z]^(T) are output values of the geomagnetic sensor.

The geomagnetic sensor calibration method may further includecalculating an average value and a standard deviation value of distancesbetween a plurality of sampled geomagnetic coordinates and the estimatedfirst central points, and determining whether calibration of thegeomagnetic sensor is necessary based on whether at least one of thecalculated average value and the standard deviation value exceeds apreset value.

The geomagnetic sensor calibration method may also include calculating apitch angle and a roll angle of an electronic device, and calculatingazimuth by using the at least one measured value of the Earth's magneticfield, the pitch angle, and the roll angle.

The controller may be a micro controller unit in the geomagnetic sensorcalibration apparatus.

The geomagnetic sensor calibration apparatus may be a remote controller.

According to an aspect of another exemplary embodiment, there isprovided a non-transitory computer readable medium which stores aprogram that is executed by a computer to perform the geomagnetic sensorcalibration method.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and/or other aspects will be more apparent by describingcertain exemplary embodiments with reference to the accompanyingdrawings, in which:

FIG. 1 is an illustration showing magnetic distortion on dimensionalcoordinates;

FIG. 2 is a diagram which illustrates effects by hard iron on threedimensional coordinates of X, Y, and Z;

FIG. 3 is a block diagram of a geomagnetic sensor calibration apparatusaccording to an exemplary embodiment;

FIG. 4 is a block diagram describing operating process of a geomagneticsensor calibration apparatus;

FIG. 5 is a block diagram of a three-axis geomagnetic sensor;

FIG. 6 is an illustration showing how a three-axis fluxgate is arranged;and

FIG. 7 is a flowchart of a geomagnetic sensor calibration methodaccording to an exemplary embodiment.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Certain exemplary embodiments will now be described in greater detailwith reference to the accompanying drawings.

In the following description, like drawing reference numerals are usedfor the same elements even in different drawings. The matters defined inthe description, such as detailed construction and elements, areprovided to assist in a comprehensive understanding of the exemplaryembodiments. However, exemplary embodiments can be practiced withoutthose specifically defined matters. Also, well-known functions orconstructions are not described in detail since they would obscure theinvention with unnecessary detail.

FIG. 3 is a block diagram of a geomagnetic sensor calibration apparatus100 according to an exemplary embodiment, FIG. 4 is a block diagramdescribing operating process of the geomagnetic sensor calibrationapparatus 100, and FIG. 5 is a block diagram of a three-axis geomagneticsensor.

Referring to FIG. 3, the geomagnetic sensor calibration apparatusaccording to an exemplary embodiment includes a geomagnetic sensor 110,an initial value estimator 120, a central point estimator 130, and acontroller 140.

The geomagnetic sensor 110 is configured to measure values of theEarth's magnetic field.

According to an exemplary embodiment, the geomagnetic sensor 110 mayinclude a three-axis geomagnetic sensor (not illustrated). Thethree-axis geomagnetic sensor calculates output values corresponding tosurrounding magnetic field by using a fluxgate of X, Y, and Z axes whichare orthogonally crossed, at 5410. Output values from the three-axisgeomagnetic sensor are values normalized by mapping output values fromthe fluxgate of X, Y, and Z axes in each within a preset range, forexample, from −1 to 1. Offset values and scale values used innormalization are previously established and stored in an internalmemory (not illustrated).

Referring to FIG. 5, the three-axis geomagnetic sensor includes adriving signal generator 111, a fluxgate of X, Y, and Z axes 112, asignal processor 113, and a geomagnetic sensor controller 114.

The driving signal generator 111 performs a role of generating drivingsignals to drive the fluxgate of X, Y, and Z axes and output the drivingsignals. The driving signals may be provided in pulse, or inversionpulse form.

The fluxgate of X, Y, and Z axes 112 includes three cores crossedorthogonally to each other and coils wound around the cores. Therefore,when driving signals are delivered to each coil, the coils are energizedand provide output values corresponding to surrounding magnetic field.

The signal processor 113 performs various processes such as amplifyingthe output values provided from the fluxgate of X, Y, and Z axes atS421, converting the amplified output values from analog values todigital values (A/D), and providing the converted amplified outputvalues to the geomagnetic sensor controller.

The geomagnetic sensor controller 114 normalizes the output values ofthe signal processor by using preset offset values and scale values andoutput the normalized values externally. Normalization may be performedthrough the following mathematical formula:

$\begin{matrix}{{{Xf}_{norm} = {\frac{\left( {{Xf} - {Xf}_{bias}} \right)}{{Xf}_{sf}}*a}}{{Yf}_{norm} = {\frac{\left( {{Yf} - {Yf}_{bias}} \right)}{{Yf}_{sf}}*a}}{{Zf}_{norm} = {\frac{\left( {{Zf} - {Zf}_{bias}} \right)}{{Zf}_{sf}}*a}}{{{Xf}_{offset} = \frac{{Xf}_{\max} + {Xf}_{\min}}{2}},{{Xf}_{sf} = \frac{{Xf}_{\max} - {Xf}_{\min}}{2}}}{{{Yf}_{offset} = \frac{{Yf}_{\max} + {Yf}_{\min}}{2}},{{Yf}_{sf} = \frac{{Yf}_{\max} - {Yf}_{\min}}{2}}}{{{Zf}_{offset} = \frac{{Zf}_{\max} + {Zf}_{\min}}{2}},{{Zf}_{sf} = \frac{{Zf}_{\max} - {Zf}_{\min}}{2}}}} & \left\lbrack {{Formula}\mspace{14mu} 3} \right\rbrack\end{matrix}$

According to Formula 3, Xf, Yf, Zf are three-axis values of the signalprocessor, Xf_(norm), Yf_(norm), Zf_(norm) are three-axis normalizingvalues, Xf_(max) and Xf_(min) are maximum value and minimum value of Xf,respectively, Yf_(max) and Yf_(min) are maximum value and minimum valueof Yf, respectively, Zf_(max) and Zf_(min) are maximum value and minimumvalue of Zf, respectively, and a is a constant value. α having a valuesmaller than 1 is used so that output values of the signal processor canbe mapped within ±1 range on horizontal axis. α can be established byusing a representative dip value of area where the azimuth calibrationdevice is used. For example, if the azimuth calibration device is usedin South Korea where the dip value is about 53°, α may be cos 53°≈0.6.Xf_(max), Xf_(min), Yf_(max), Yf_(min), Zf_(max), and Zf_(min) areestablished by previously measuring output values while rotating theazimuth calibration device at least once, and by selecting maximum andminimum values among the output values. Because established a, Xf_(max),Xf_(min), Yf_(max), Yf_(min), Zf_(max), and Zf_(min) values are storedin a memory (not illustrated) within the three-axis geomagnetic sensoror in an external memory (not illustrated), they can be used duringnormalization.

Although not illustrated in the drawings, converting sensor axes may beperformed when need arises, at S421. In other words, converting axes ofthe three-axis geomagnetic sensor into axes defined from a viewpoint ofan input device, may be performed.

Electrical noises and high frequency noises are removed through a lowpass filter, at S422.

FIG. 6 is an illustration showing how the three-axis fluxgate isarranged. Referring to FIG. 6, the X axis of the fluxgate within thethree-axis geomagnetic sensor is mounted toward a direction of a frontpart of the geomagnetic sensor calibration apparatus 100 including thefluxgate, the Y axis of the fluxgate is mounted toward a direction of aside part, and X and Y axes of the fluxgate are mounted to be crossedorthogonally on a plane where the geomagnetic sensor calibrationapparatus 100 is disposed. The Z axis of the fluxgate is mounted towarda direction orthogonal to the plane where the geomagnetic sensorcalibration apparatus 100 is disposed.

The initial value estimator 120 estimates first central points from themeasured values of the Earth's magnetic field by using a first linearfunction. A sphere equation having central points (X₀, Y₀, Z₀) andradius (r) is the same as Formula 2 described above. Accordingly, anypoint on the sphere can be interpreted as satisfying the function.Regarding three-axis geomagnetic sensor data that satisfy conditionsdefined in Formula 1, when output values are (X_(i), Y_(i), Z_(i)),relations between the output values and the radius (r_(i)) may beexpressed as:

r _(i)=√{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)²)},

When a function f is defined as f=r_(i) ²−r² for the initial valueestimator, the function f can be organized according to the followingmathematical formula:

f=(X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)² −r ²=−2(X _(i) X ₀ +Y_(i) Y ₀ +Z _(i) Z ₀)+p+(X _(i) ² +Y _(i) ² +Z _(i) ²),  [Formula 4]

wherein ρ=X₀ ²+Y₀ ²+Z₀ ²−r². Variable p is used to linearize thefunction f.

The following Formula (Formula 5) may be expressed when the function ofFormula 4 is expanded to n number of data classes:

$\begin{matrix}{{{{{AP} - B} = F},{wherein}}{{A = \begin{bmatrix}{{- 2}X_{1}} & {{- 2}Y_{1}} & {{- 2}Z_{1}} & 1 \\{{- 2}X_{2}} & {{- 2}Y_{2}} & {{- 2}Z_{2}} & 1 \\\vdots & \vdots & \vdots & \vdots \\{{- 2}X_{n}} & {{- 2}Y_{n}} & {{- 2}Z_{n}} & 1\end{bmatrix}},{P = \begin{bmatrix}X_{0} \\Y_{0} \\Z_{0} \\p\end{bmatrix}},{B = \begin{bmatrix}{X_{1}^{2} + Y_{1}^{2} + Z_{1}^{2}} \\{X_{2}^{2} + Y_{2}^{2} + Z_{2}^{2}} \\\vdots \\{X_{n}^{2} + Y_{n}^{2} + Z_{n}^{2}}\end{bmatrix}},{F = \begin{bmatrix}f_{1} \\f_{2} \\\vdots \\f_{n}\end{bmatrix}}}} & \left\lbrack {{Formula}\mspace{14mu} 5} \right\rbrack\end{matrix}$

When F=0 is defined for the least square solution, AP-B=0 in Formula 5and P=(A^(T)A)⁻¹A^(T)B. Examples of the least squre fitting method aredescribed in detail in the article, “AN ALGORITHM FOR FITTING OFSPHERES” by Ik-Sung Kim, J. Korea Soc. Math. Educ. Ser. B: Pure Appl.Math. Volume 11, Number 1 (February 2004), Pages 37-49, herebyincorporated by reference.

X₀, Y₀, Z₀, and ρ are calculated with the above P value, and r iscalculated according to definition of ρ, ρ=X₀ ²+Y₀ ²+Z₀ ²−r². Asdescribed in more detail below, when the calculated initial value r isr₀, the central point estimator 130 calculates second central points byusing the initial values, X₀, Y₀, Z₀, and r₀ which are obtained by theabove.

The central point estimator 130 estimates second central points by usinga second linear function and the above estimated initial values. Afterestimating the initial values, final estimating central points isperformed based on the estimated initial values, at S430.

In order to search final central points from the estimated initialvalues, X₀, Y₀, Z₀, and r₀, a Gauss-Newton algorithm is used. TheGauss-Newton algorithm is a method to search solutions by linearizing anon-linear function and repeating the processes. In one exemplaryembodiment, a minimized function is established to be d_(i)=r_(i)−r₀ soas to apply a Gauss-Newton algorithm. Herein, r_(i)=√{square root over((X_(i)−X₀)²+(Y_(i)−Y₀)²+(Z_(i)−Z₀)²)}{square root over((X_(i)−X₀)²+(Y_(i)−Y₀)²+(Z_(i)−Z₀)²)}{square root over((X_(i)−X₀)²+(Y_(i)−Y₀)²+(Z_(i)−Z₀)²)}.

A Jacobian matrix (J) regarding the minimized function d_(i) iscalculated with a following equation:

$\begin{matrix}{J = {\begin{bmatrix}\frac{\partial d_{1}}{\partial X_{0}} & \frac{\partial d_{1}}{\partial Y_{0}} & \frac{\partial d_{1}}{\partial Z_{0}} & \frac{\partial d_{1}}{\partial r_{0}} \\\frac{\partial d_{2}}{\partial X_{0}} & \frac{\partial d_{2}}{\partial Y_{0}} & \frac{\partial d_{2}}{\partial Z_{0}} & \frac{\partial d_{2}}{\partial r_{0}} \\\vdots & \vdots & \vdots & \vdots \\\frac{\partial d_{n}}{\partial X_{0}} & \frac{\partial d_{n}}{\partial Y_{0}} & \frac{\partial d_{n}}{\partial Z_{0}} & \frac{\partial d_{n}}{\partial r_{0}}\end{bmatrix} = {\quad\begin{bmatrix}\frac{- \left( {X_{1} - X_{0}} \right)}{r_{1}} & \frac{- \left( {Y_{1} - Y_{0}} \right)}{r_{1}} & \frac{- \left( {Z_{1} - Z_{0}} \right)}{r_{1}} & {- 1} \\\frac{- \left( {X_{2} - X_{0}} \right)}{r_{2}} & \frac{- \left( {Y_{2} - Y_{0}} \right)}{r_{2}} & \frac{- \left( {Z_{2} - Z_{0}} \right)}{r_{2}} & {- 1} \\\vdots & \vdots & \vdots & \vdots \\\frac{- \left( {X_{n} - X_{0}} \right)}{r_{n}} & \frac{- \left( {Y_{n} - Y_{0}} \right)}{r_{n}} & \frac{- \left( {Z_{n} - Z_{0}} \right)}{r_{n}} & {- 1}\end{bmatrix}}}} & \left\lbrack {{Formula}\mspace{14mu} 6} \right\rbrack\end{matrix}$

When the linearized equation JP=−d is solved with the least squaremethod, P=(J^(T)J)⁻¹J^(T)(−d). Herein, P and d are as follows:

$\begin{matrix}{{P = \begin{bmatrix}p_{X_{0}} \\p_{Y_{0}} \\p_{Z_{0}} \\p_{r_{0}}\end{bmatrix}},{d = \begin{bmatrix}{r_{1} - r_{0}} \\{r_{2} - r_{0}} \\\vdots \\{r_{n} - r_{0}}\end{bmatrix}}} & \left\lbrack {{Formula}\mspace{14mu} 7} \right\rbrack\end{matrix}$

Updating parameters is performed by using previous values and P value.

X ₀ =X ₀ +p _(X) ₀

Y ₀ =Y ₀ +p _(Y) ₀

Z ₀ =Z ₀ +p _(Z) ₀

r ₀ =r ₀ +p _(r) ₀   [Formula 8]

Final central points (X₀, Y₀, Z₀) are calculated by repeating formulae 6to 8 until it satisfies convergence conditions. Convergence conditionsare as follows. Herein, ε₁ is a constant value previously established.

∥P∥=√{square root over (p _(X) ₀ ² +p _(Y) ₀ ² +p _(Z) ₀ ² +p _(r) ₀²)}<ε₁[Formula 9]

The following describes the controller 140. The controller 140determines whether calibrating the geomagnetic sensor 110 is necessarybased on the first estimated central points. When calibrating isdetermined to be necessary, the controller 140 controls estimating thesecond central points.

The controller 140 calculates distance of the coordinates of X, Y, and Zsensed by the geomagnetic sensor from Formula 1 based on the obtainedfirst central points, X₀, Y₀, Z₀. When the distance is determined to bemore than allowable range α, the controller 140 determines that thegeomagnetic values have distortion and starts calibrating. When thedistance is within allowable range α, the controller 140 determines thaterrors of the geomagnetic sensor are not detected. However, the aboveprocess may be performed per preset time interval, in which casecalibrating starts when the obtained distance exceeds allowable range αfor the preset time interval.

When the offset values are distorted, the controller 140 controls thegeomagnetic sensor 110 to sample a plurality of geomagnetic sensorvalues. The geomagnetic sensor 110 outputs a plurality of sampled valuesby repeatedly sampling values outputted from the three-axis geomagneticsensor (not illustrated). The sampling process may be performed forcertain time. Thus, when a certain time after first sampling passes,first sampling is newly performed and the previous first sampled valuesare deleted. The number of samplings may be previously established suchthat the sampling stops after the previously established value.

The distances between sampled values may be more than a specificdistance so as to precisely examine whether the offset values aredistorted. Therefore, when values sampled at an i-th number are Si,distance between S1 and S2 is calculated and compared with a presetcritical distance when S2 is sampled. When the distance is within acritical distance, S2 is newly sampled. When the distance is not withina critical distance, S2 is selected and S3 is sampled. When S3 issampled, distance between 51 and S3 and distance between S2 and S3 areconsecutively calculated, and the calculated distance of each of themcompared with a critical distance. When any one of them is within acritical distance, S3 is newly sampled. When both of them are out of thecritical distance, S3 is selected. According to the same method, S1˜SNare outputted by sampling until the sampling number that a userestablishes (N number).

The controller 140 calculates distance from each of sampled S1˜SN to theoffset values calculated above in the geomagnetic sensor 110 andcalculates an average value and a standard deviation value of thedistances. When any one of the average value and the standard deviationvalue is more than a predefined value, it determines that distortion hasoccurred. However, when both of the average value and the standarddeviation value are less than a preset value, calibrating stops becausedistortion is determined to be not detected. When distortion of theoffset values is determined to be detected, the controller 140 controlsthe central point estimator 130 to estimate the above second centralpoints.

The controller 140 calibrates geomagnetic sensor values by using thecentral points, M₀=[X₀, Y₀, Z₀]^(T), which are calculated in the centralpoint estimator, at S440. Output values of the three-axis geomagneticsensor which are orthogonal to each other are M_(b)=[X, Y, Z]^(T), andgeomagnetic sensor values are calibrated by using a following formula:

$\begin{matrix}{{\hat{M}}_{b} = {{M_{b} - M_{0}} = \begin{bmatrix}{X - X_{0}} \\{Y - Y_{0}} \\{Z - Z_{0}}\end{bmatrix}}} & \left\lbrack {{Formula}\mspace{14mu} 10} \right\rbrack\end{matrix}$

Calculation errors are minimal even when r₀ is fixed to be constant fromthe initial estimated values, X₀, Y₀, Z₀, and r₀. When a radius isfixed, calculating speed is faster because algorithm calculations toestimate central points become simpler. Accordingly, a micro controllerunit (MCU), which has limited calculating performance, can be used. Forexample, it is possible to fix a radius value (r) as magnitude of theEarth's magnetic field in calculating to search offset values of thethree-axis geomagnetic sensor. Magnitude of the Earth's magnetic fieldis different according to latitude (usually 0.25˜0.65 Gauss); however,it is averagely about 0.5 Gauss. Therefore, magnitude of the Earth'smagnetic field may be fixed based on 0.5 Gauss, and central points, X0,Y0, Z0, may be calculated by applying a Gauss-Newton algorithm.

The above described Jacobian matrix can be obtained as follows.

A Jacobian matrix regarding the minimized function, d_(i)=r_(i)− r, iscalculated in the following mathematical formula. Herein,

r _(i)=√{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)²)},

$\begin{matrix}{J = {\begin{bmatrix}\frac{\partial d_{1}}{\partial X_{0}} & \frac{\partial d_{1}}{\partial Y_{0}} & \frac{\partial d_{1}}{\partial Z_{0}} \\\frac{\partial d_{2}}{\partial X_{0}} & \frac{\partial d_{2}}{\partial Y_{0}} & \frac{\partial d_{2}}{\partial Z_{0}} \\\vdots & \vdots & \vdots \\\frac{\partial d_{n}}{\partial X_{0}} & \frac{\partial d_{n}}{\partial Y_{0}} & \frac{\partial d_{n}}{\partial Z_{0}}\end{bmatrix} = {\quad\begin{bmatrix}\frac{- \left( {X_{1} - X_{0}} \right)}{r_{1}} & \frac{- \left( {Y_{1} - Y_{0}} \right)}{r_{1}} & \frac{- \left( {Z_{1} - Z_{0}} \right)}{r_{1}} \\\frac{- \left( {X_{2} - X_{0}} \right)}{r_{2}} & \frac{- \left( {Y_{2} - Y_{0}} \right)}{r_{2}} & \frac{- \left( {Z_{2} - Z_{0}} \right)}{r_{2}} \\\vdots & \vdots & \vdots \\\frac{- \left( {X_{n} - X_{0}} \right)}{r_{n}} & \frac{- \left( {Y_{n} - Y_{0}} \right)}{r_{n}} & \frac{- \left( {Z_{n} - Z_{0}} \right)}{r_{n}}\end{bmatrix}}}} & \left\lbrack {{Formula}\mspace{14mu} 11} \right\rbrack\end{matrix}$

When the linear equation, JP=−d, is solved with the least square method,P=(J^(T)J)⁻¹J^(T)(−d). Herein, P and d are as follows:

$\begin{matrix}{{P = \begin{bmatrix}p_{x_{0}} \\p_{y_{0}} \\p_{z_{0}}\end{bmatrix}},{d = \begin{bmatrix}{r_{1} - \overset{\_}{r}} \\{r_{2} - \overset{\_}{r}} \\\vdots \\{r_{n} - \overset{\_}{r}}\end{bmatrix}}} & \left\lbrack {{Formula}\mspace{14mu} 12} \right\rbrack\end{matrix}$

Updating parameters is performed by using P value and previous values.

X ₀ =X ₀ −p _(x) ₀

Y ₀ =Y ₀ −p _(y) ₀

Z ₀ =Z ₀ −p _(z) ₀   [Formula 13]

Final central points, X0, Y0, Z0, are calculated by repeating the aboveprocesses until it satisfies convergence conditions. Convergenceconditions are expressed in a following mathematical formula. ε₂ is apreviously established constant value.

∥P∥=√{square root over (p _(x) ₀ ² +p _(y) ₀ ² +p _(z) ₀ ²)}<ε₂[Formula14]

The geomagnetic sensor calibration apparatus 100 described above mayfurther include a storage (not illustrated).

The storage (not illustrated) stores geomagnetic values sensed by thegeomagnetic sensor 110, initial estimated values X0, Y0, Z0, and r0calculated by the initial value estimator 120, a standard deviationvalue and an average value of distances between the sensed geomagneticvalues and offset values which are calculated by the controller 140,other data necessary for estimating central points, and result values.The storage may be implemented as non-transitory readable recordingmedium.

Non-transitory readable medium indicates a medium which stores datasemi-permanently and can be read by devices. For example, non-transitoryreadable medium may be CD, DVD, hard disk, Blu-ray disk, USB, memorycard, or ROM.

When estimating central points is completed, the controller 140calculates azimuth by using three-axis geomagnetic output valuesoutputted from the three-axis geomagnetic sensor, a pitch angle and aroll angle calculated in a tilt angle calculator (not illustrated).Calculating azimuth may be performed by using a following mathematicalformula:

$\begin{matrix}{\psi = {{\tan^{- 1}\left( \frac{{Y_{norm}*\cos \; \varphi} - {Z_{norm}*\sin \; \varphi}}{\begin{matrix}{{X_{norm}*\cos \; \theta} - {Y_{norm}*\sin \; \theta*\sin \; \varphi} -} \\{Z_{norm}*\sin \; \theta*\cos \; \varphi}\end{matrix}} \right)}.}} & \left\lbrack {{Formula}\mspace{14mu} 15} \right\rbrack\end{matrix}$

wherein ψ is azimuth, X_(norm), Y_(norm), and Z_(norm) are three-axisgeomagnetic output values which are normalized by using calibratedoffset values in each, θ is a pitch angle, and φ is a roll angle. Thecontroller 140 can calculate azimuth precisely because the values arenormalized according to the offset values of which distortion iscalibrated.

In the following, a method of calibrating errors of the geomagneticsensor according to an exemplary embodiment is described.

FIG. 7 is a flowchart describing the geomagnetic sensor calibrationmethod according to an exemplary embodiment.

Referring to FIG. 7, the geomagnetic sensor calibration method accordingto an exemplary embodiment includes measuring the geomagnetic field atoperation S710, estimating first central points at operation S720,determining whether calibration is necessary at operation S730, and ifcalibration is determined to be necessary, estimating second centralpoints at operation S740.

At operation S710, values of the Earth's magnetic field are measured.The three-axis geomagnetic sensor may be used to measure the Earth'smagnetic field. Constitutions and operations of the three-axisgeomagnetic sensor are previously described in exemplary embodiments andwill not be further explained.

At operation S720, first central points of the measured values of theEarth's magnetic field are estimated by using the first linear function.Herein, the first linear function is a function which linearizes thefunction

f=r _(i) ² −r ².

Herein,

r _(i)=√{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)²)},

(X−X ₀)²+(Y−Y ₀)²+(Z−Z ₀)² =r ²,

(X_(i), Y_(i), z_(i)) are coordinate values which are sampled at an i-thnumber in the three-axis geomagnetic sensor,

(X₀, Y₀, Z₀) are the first central points, and

1≦i≦n.

Explanation of specific equations is previously described in exemplaryembodiments of the geomagnetic sensor calibration apparatus and will notbe further described.

At operation S730, necessity of calibration is determined. An averagevalue and a standard deviation value of distances between a plurality ofgeomagnetic field sampling coordinates and the estimated first centralpoints are obtained. Necessity of calibrating is determined according towhether at least one of the calculated average value and the standarddeviation value exceeds a preset value. The specific method ofdetermining whether distortion has occurred is previously described inexemplary embodiments of the geomagnetic sensor calibration apparatusand will not be further described.

At operation S740, second central points are estimated by using thesecond linear function and the above estimated first central points. Thesecond linear function is a function which linearizes the minimizedfunction

d _(i) =r _(i) −r ₀.

Herein,

r _(i)=√{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)²)},

(X_(i), Y_(i), Z_(i)) are coordinate values which are sampled at an i-thnumber in the three-axis geomagnetic sensor,

(X₀, Y₀, Z₀) are the estimated first central points,

r₀ is a radius of the sphere having the estimated first central points,and

1≦i≦n.

Explanation of specific equations is previously described in exemplaryembodiments of the geomagnetic sensor calibration apparatus, which willnot be further described.

Further, the first linear function is a function which linearizes theminimized function,

d _(i) =r _(i) − r.

Herein,

r _(i)=√{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)²)},

(X_(i), Y_(i), Z_(i)) are coordinate values which are sampled at an i-thnumber in the three-axis geomagnetic sensor,

(X₀, Y₀, Z₀) are the estimated first central points,

r is a constant value which indicates a radius of the sphere having thefirst central points, and

1≦i≦n.

When a radius is fixed, algorithm calculations to estimate centralpoints are simpler and calculating speed becomes faster. Specificexplanation of equations is previously described in exemplaryembodiments of the geomagnetic sensor calibration apparatus and will notbe further described.

Although not described in the drawings, the above calibration method ofthe geomagnetic sensor may further include calibrating central points byusing the following mathematical formula:

${{\hat{M}}_{b} = {{M_{b} - M_{0}} = \begin{bmatrix}{X - X_{0}} \\{Y - Y_{0}} \\{Z - Z_{0}}\end{bmatrix}}},$

wherein M₀=[X₀, Y₀, Z₀]^(T) are the above estimated second centralpoints, and

M_(b)=[X, Y, Z]^(T) are output values of the three-axis geomagneticsensor.

The geomagnetic sensor calibration method may further includecalculating (not illustrated) a pitch angle and a roll angle of anelectronic device, and calculating azimuth by using the measured valuesof the Earth's magnetic field, the pitch angle and the roll angle.

The geomagnetic sensor calibration method may be implemented as programswhich include algorithms that can run on a computer including aprocessor, and the programs may be stored and provided in non-transitorycomputer readable medium.

Non-transitory computer readable medium indicate medium which store datasemi-permanently and can be read by devices. Specifically, the abovevarious applications or programs may be stored and provided innon-transitory readable medium, such as CD, DVD, hard disk, Blu-raydisk, USB, memory card, or ROM.

According to the various exemplary embodiments, initial central pointsof the sphere which models the sensed geomagnetic values are estimatedby using linear functions in circumstances having effects by hard iron.Further, by estimating final central points with the estimated initialcentral points, calibration can be performed quickly and precisely.

Further, because the amount of calculations is reduced by fixing aradius value as constant, calibrating the geomagnetic sensor may beperformed more quickly and efficiently.

The foregoing exemplary embodiments and advantages are merely exemplaryand are not to be construed as limiting the present invention. Thepresent teaching can be readily applied to other types of apparatuses.Also, the description of the exemplary embodiments is intended to beillustrative, and not to limit the scope of the claims, and manyalternatives, modifications, and variations will be apparent to thoseskilled in the art.

What is claimed is:
 1. A geomagnetic sensor calibration apparatuscomprising: a geomagnetic sensor configured to measure at least onevalue of Earth's magnetic field; an initial value estimator configuredto estimate first central points from the at least one measured value ofthe Earth's magnetic field by using a first linear function; a centralpoint estimator configured to estimate second central points by using asecond linear function and the estimated first central points; and acontroller configured to determine whether calibration of thegeomagnetic sensor is necessary based on the estimated first centralpoints, and control the central point estimator to estimate secondcentral points based on a result of the determination.
 2. Thegeomagnetic sensor calibration apparatus of claim 1, wherein the atleast one value of the Earth's magnetic field is expressed withcoordinates in an X, Y, and Z coordinate space.
 3. The geomagneticsensor calibration apparatus of claim 1, wherein the first linearfunction linearizes a function:f=r _(i) ² −r ²,whereinr _(i)=√{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)²)},(X−X ₀)²+(Y−Y ₀)²+(Z−Z ₀)² =r ², (X_(i), Y_(i), Z_(i)) are coordinatevalues sampled at an i-th number of the geomagnetic sensor, (X₀, Y₀, Z₀)are the estimated first central points, n is a predetermined integer,and 1≦i≦n.
 4. The geomagnetic sensor calibration apparatus of claim 1,wherein the second linear function linearizes a minimized function:d _(i) =r _(i) −r ₀,whereinr _(i)=√{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)²)},(X_(i), Y_(i), Z_(i)) are coordinate values sampled at an i-th number ofthe geomagnetic sensor, (X₀, Y₀, Z₀) are the estimated first centralpoints, r₀ is a radius of a sphere having the estimated first centralpoints, n is a predetermined integer, and 1≦i≦n.
 5. The geomagneticsensor calibration apparatus of claim 1, wherein the first linearfunction linearizes a minimized function:d _(i) =r _(i) − r ,whereinr _(i)=√{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)²)},(X_(i), Y_(i), Z_(i)) are coordinate values sampled at an i-th number ofthe geomagnetic sensor, (X₀, Y₀, Z₀) are the estimated first centralpoints, r₀ is a constant value indicating a radius of a sphere havingthe estimated first central points, n is a predetermined integer, and1≦i≦n.
 6. The geomagnectic sensor calibration apparatus of claim 1,wherein the controller is further configured to calibrate central pointsby using a formula: ${{\hat{M}}_{b} = {{M_{b} - M_{0}} = \begin{bmatrix}{X - X_{0}} \\{Y - Y_{0}} \\{Z - Z_{0}}\end{bmatrix}}},$ wherein M₀=[X₀, Y₀, Z₀]^(T) are coordinate valuesindicating central points estimated by the central point estimator, andM_(b)=[X, Y, Z]^(T) are output values of the geomagnetic sensor.
 7. Thegeomagnetic sensor calibration apparatus of claim 1, wherein thecontroller is further configured to calculate a mean value and astandard deviation value of distances between a plurality of samplingcoordinates output from the geomagnetic sensor and the estimated firstcentral points, and determine whether calibration of the geomagneticsensor is necessary based on whether at least one of the calculatedaverage value and standard deviation value exceeds a preset value. 8.The geomagnetic sensor calibration apparatus of claim 1, wherein thegeomagnetic sensor comprises: a fluxgate of X, Y, and Z axes which arearranged orthogonally to each other; a driving signal generatorconfigured to provide driving signals to the fluxgate of X, Y, and Zaxes; a signal processor configured to, when the fluxgate of X, Y, and Zaxes is driven by the driving signals and outputs electrical signalscorresponding to surrounding magnetic field, convert the electricalsignals to digital signals and output the digital signals; and ageomagnetic sensor controller configured to perform normalization to mapoutput values of the signal processor within a certain range by usingoffset values and preset scale values, and output normalized three-axisoutput values.
 9. The geomagnetic sensor calibration apparatus of claim1, wherein the controller is further configured to calculate a pitchangle and a roll angle of the geomagnetic sensor calibration apparatus,and calculate azimuth by using the at least one measured value of theEarth's magnetic field, the pitch angle, and the roll angle.
 10. Thegeomagnetic sensor calibration apparatus of claim 5, wherein thecontroller comprises a micro controller unit.
 11. The geomagnetic sensorcalibration apparatus in claim 1, wherein the geomagnetic sensorcalibration apparatus comprises a remote controller.
 12. A geomagneticsensor calibration method comprising: measuring at least one value ofEarth's magnetic field; estimating first central points from the atleast one measured value of the Earth's magnetic field by using a firstlinear function; and estimating second central points by using a secondlinear function and the estimated first central points.
 13. Thegeomagnetic sensor calibration method of claim 12, wherein the at leastone measured value of the Earth's magnetic field is expressed withcoordinates in an X, Y, and Z coordinate space.
 14. The geomagneticsensor calibration method of claim 12, wherein the first linear functionlinearizes a function:f _(i) =r _(i) ² −r ²,whereinr _(i)=√{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)²)},(X−X ₀)²+(Y−Y ₀)²+(Z−Z ₀)² =r ², (X_(i), Y_(i), Z_(i)) are coordinatevalues sampled at an i-th number of the geomagnetic sensor, (X₀, Y₀, Z₀)are the estimated first central points, n is a predetermined integer,and 1≦i≦n.
 15. The geomagnetic sensor calibration method of claim 12,wherein the second linear function linearizes a minimized function:d _(i) =r _(i) − r ,whereinr _(i)=√{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)²)},(X_(i), Y_(i), Z_(i)) are coordinate values sampled at an i-th number ofthe geomagnetic sensor, (X₀, Y₀, Z₀) are the estimated first centralpoints, r₀ is a constant value indicating a radius of a sphere havingthe estimated first central points, n is a predetermined integer, and1≦i≦n.
 16. The geomagnetic sensor calibration method of claim 12,wherein the first linear function linearizes a minimized function:d _(i) =r _(i) − r ,whereinr _(i)=√{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z₀)²)}{square root over ((X _(i) −X ₀)²+(Y _(i) −Y ₀)²+(Z _(i) −Z ₀)²)},(X_(i), Y_(i), Z_(i)) are coordinate values sampled at an i-th number ofthe geomagnetic sensor, (X₀, Y₀, Z₀) are the estimated first centralpoints, r is a constant value indicating a radius of a sphere having theestimated first central points, n is a predetermined integer, and 1≦i≦n.17. The geomagnetic sensor calibration method of claim 12, furthercomprising: calibrating central points by using a formula:${{\hat{M}}_{b} = {{M_{b} - M_{0}} = \begin{bmatrix}{X - X_{0}} \\{Y - Y_{0}} \\{Z - Z_{0}}\end{bmatrix}}},$ wherein M₀=[X₀, Y₀, Z₀]^(T) are coordinate values ofthe second central points estimated by the central point estimator, andM_(b)=[X, Y, Z]^(T) are output values of the geomagnetic sensor.
 18. Thegeomagnetic sensor calibration method of claim 12, further comprising:calculating an average value and a standard deviation value of distancesbetween a plurality of sampled geomagnetic coordinates and the estimatedfirst central points; and determining whether calibration of thegeomagnetic sensor is necessary based on whether at least one of thecalculated average value and the standard deviation value exceeds apreset value.
 19. The geomagnetic sensor calibration method of claim 12,further comprising: calculating a pitch angle and a roll angle of anelectronic device; and calculating azimuth by using the at least onemeasured value of the Earth's magnetic field, the pitch angle, and theroll angle.
 20. A non-transitory computer readable medium which stores aprogram that is executed by a computer to perform the geomagnetic sensorcalibration method of claim 12.